MHD/Shocks: MHD Wave Case Studies

Magnetohydrodynamic (MHD) waves, are low-frequency waves (f ≪ ion gyrofrequency)
in the plasma. In this module, we examine small amplitude waves propagating in a
homogeneous, isotropic, and uniformly magnetized plasma. Unlike the shock wave treated
elsewhere, in this module the wave does not alter the properties of the medium through
which it passes. The program solves for the phase velocity and group velocity of
the waves based on the properties of the plasma. The velocities for three MHD wave
modes, fast, intermediate, and slow, are calculated by the program. A fourth mode
is sometimes discussed, called the entropy fluctuation. This mode does not propagate.

Enter the parameters of the plasma on the left-hand side of the window. The defaults
correspond to typical values in the solar wind. These parameters include: the magnetic
field strength in nT, number density of the plasma in #/cm3, electron
and ion γ (the ratio of specific heats) and temperature in K, and the ion
mass in units of the mass of a proton. The electrons and ions are handled separately
to allow different ratios of specific heat in the calculation of the sound speed.
Click Calculate to display phase velocities and
group velocities of the three MHD wave modes in km/s. The parameter θBk
gives the direction of the magnetic field relative to the phase front of the wave.
The group velocity need not propagate along the phase velocity. Thus it must be
specified by two components, here given as along the field and perpendicular to
it.